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Kripke argued that there might not have been unicorns: since unicorns are fictional species, they are necessarily fictional. There are three arguments aimed at showing the fictionality of unicorns, but all of them fail. There would be unicorns if there were a single species or genus of animals resembling the unicorns of pictures. This also serves as an instructive example of the failure of the accessibility relation between possible worlds to be both transitive and symmetrical.

Kripke argued that there might not have been unicorns: since unicorns are fictional species, they are necessarily fictional. There are three arguments aimed at showing the fictionality of unicorns, but all of them fail. There would be unicorns if there were a single species or genus of animals resembling the unicorns of pictures. This also serves as an instructive example of the failure of the accessibility relation between possible worlds to be both transitive and symmetrical.